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Kececioglu's rank-adjustment example: median ranks of three failures among two suspensions

ToolWeibull Life Analysis
SourceReliaSoft Corporation (2015). "Parameter Estimation." ReliaWiki (Life Data Analysis Reference). Rank adjustment example (after Kececioglu), five units F S F S F at 5,100 / 9,500 / 15,000 / 22,000 / 40,000 hr (copy in References/Weibull/ReliaWiki/).
LevelUndergraduate

Problem

Five units were tested: failures at 5,100, 15,000 and 40,000 hours and suspensions (removed unfailed) at 9,500 and 22,000 hours. Using Johnson's rank-adjustment method, find the mean order number of each failure and its median rank for plotting.

Inputs to Enter

  • Life data: 5100 F; 9500 S; 15000 F; 22000 S; 40000 F
  • Primary method: rank regression; median ranks exact (or Bernard)
Open the Weibull Life Analysis tool

Answers

  • Mean order numbers 1, 2.25 and 4.125 (increment I = (N + 1 − previous MON)/(1 + units beyond the present suspended set))
  • Median ranks 13 %, 36 % and 71 % (exact); Bernard's approximation for MON 2.25 of 5: (2.25 − 0.3)/5.4 = 0.3611
  • Suspensions carry no rank

Notes

Paste the five lines; the rank table shows the mean order numbers and both median ranks. Reproduced exactly for the order numbers and within 0.5 % for the median ranks (test_weibull.php).

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